I want to calculate the subsurface flow from the upper parts of the watershed which can enter the Vadose zone in the plain. As this is just a very little portion of my study, I have no time to run a complex and time consuming model. Therefore, can anybody introduce me a simple model or equation by which I can estimate the subsurface flow?
Dear Vahid, this is an idea that was proposed by Anders Worman in a paper in WRR. I translate it in a much simpler fashion that maybe can fit your case. Let us suppose that we are at steady state. If you have a digital elevation model of the watershed, and if you can estimate the permeability of the soil and its thickness on the hillslope, you can compute the soil gradient from the dem and assume that it is also the hydraulic gradient in the subsurface flow on the hillslope. Then using the Darcy's law you can sum the contribution from the different hillslope along each steepest gradient direction and obtain the overall subsurface contribution.
Possibly this is not the simplest way but it captures a relevant feature that is the hydraulic gradient, whose proxy is here the slope gradient. I hope this can be of help
Marco
Dr. Marco Pilotti
Thank you so mach for your valuable comment. Could you please give me the full address of the mentioned article so that I can download it.
Exact three‐dimensional spectral solution to surface‐groundwater interactions with arbitrary surface topography
A Wörman, AI Packman, L Marklund, JW Harvey, SH Stone
Geophysical research letters 33 (7)
Dear Vahid,
Here, in this book, a simple method that can help.
https://books.google.dz/books?id=tLHefCIWKJgC&pg=PA9&lpg=PA9&dq=calculating+subsurface+flow?&source=bl&ots=vgs83LEI3T&sig=BlrD7emm1gF2Ito4KAn9JiVgYTE&hl=fr&sa=X&ved=0ahUKEwiPguHh98bPAhXC0xoKHbN4AogQ6AEIWTAH#v=onepage&q=calculating%20subsurface%20flow%3F&f=false
With my best regards
Prof. Bachir ACHOUR
Vahid, Pl see the attached paper, if it would help. Best,
Article Groundwater resources assessment of the Koyna River Basin, India
I think that you are well-armed by the responses that you have already received but you need to interrogate the watershed and its geology to be sure you understand the processes by which water is reaching the down-gradient vadose zone. Are you working in an arid or wet environment? Are you concerned with only soil and alluvium or do you have a bedrock vadose zone or perhaps an aquifer? Are there gaining or losing streams in the watershed? Vegetation also is important both as preventing runoff and consuming water through evaportranspiration. Each watershed is unique and you need to assess its "big-picture" attributes and properties before you can determine down-gradient flow.
I am also often confuse by the questions of my hydrologists colleagues, especially modellers. They want to calculate all, ...once I add a phone call from a colleague who ask me for a model the average macroporosity of an entire catchment, he was very serious and do not understand why I was schoked by his question.
So... I fully agree with Dwight as he is geologist like me.
You have to assess the "big picture", for that I I recommend you this paperwhere hydrologist and geologist worked together to catch the big pictures from a step by step procedures, from map, to field work and finally modelling.
Indeed you subsurface flow can be close to null in sandy and permeable soil and high on impermebale substratum like marls, claystone,etc... as express by Dwight you can have a look to the drainage density (number osf stream per surface) which will give you a first "proxy" on te permability of the substratum, the latter can also be asses by looking at geological maps.
Best regards
Article Towards more systematic perceptual model development: A case...
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